相关论文: A Machine Learning Enhanced Algorithm for the Opti…

We apply a physics-informed neural network (PINN) to solve the two-point boundary value problem (BVP) arising from the necessary conditions postulated by Pontryagin's Minimum Principle for optimal control. Such BVPs are known to be…

This paper presents a novel deep learning framework for solving multiple optimal stopping problems in high dimensions. While deep learning has recently shown promise for single stopping problems, the multiple exercise case involves complex…

This paper studies a vertical powered descent problem in the context of planetary landing, considering glide-slope and thrust pointing constraints and minimizing any final cost. In a first time, it proves the Max-Min-Max or Max-Singular-Max…

In this paper, the scheduling problems of landing and takeoff aircraft on a same runway and on dual runways are addressed. In contrast to the approaches based on mixed-integer optimization models in existing works, our approach focuses on…

Optimal balance is a non-asymptotic numerical method to compute a point on the slow manifold for certain two-scale dynamical systems. It works by solving a modified version of the system as a boundary value problem in time, where the…

The boundary control problem is a non-convex optimization and control problem in many scientific domains, including fluid mechanics, structural engineering, and heat transfer optimization. The aim is to find the optimal values for the…

In the field of autonomous Unmanned Aerial Vehicles (UAVs) landing, conventional approaches fall short in delivering not only the required precision but also the resilience against environmental disturbances. Yet, learning-based algorithms…

The next generation of Mars rotorcrafts requires on-board autonomous hazard avoidance landing. To this end, this work proposes a system that performs continuous multi-resolution height map reconstruction and safe landing spot detection.…

This paper presents a computationally efficient algorithm for eco-driving over long prediction horizons. The eco-driving problem is formulated as a bi-level program, where the bottom level is solved offline, pre-optimizing gear as a…

We propose a novel randomized linear programming algorithm for approximating the optimal policy of the discounted Markov decision problem. By leveraging the value-policy duality and binary-tree data structures, the algorithm adaptively…

We propose a machine learning algorithm for solving finite-horizon stochastic control problems based on a deep neural network representation of the optimal policy functions. The algorithm has three features: (1) It can solve…

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

Recent work linking deep neural networks and dynamical systems opened up new avenues to analyze deep learning. In particular, it is observed that new insights can be obtained by recasting deep learning as an optimal control problem on…

In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…

We propose an approach based on machine learning to solve two-stage linear adaptive robust optimization (ARO) problems with binary here-and-now variables and polyhedral uncertainty sets. We encode the optimal here-and-now decisions, the…

We study the existing algorithms that solve the multidimensional martingale optimal transport. Then we provide a new algorithm based on entropic regularization and Newton's method. Then we provide theoretical convergence rate results and we…

This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic…

In this paper, the trajectory planning problem for autonomous rendezvous and docking between a controlled spacecraft and a tumbling target is addressed. The use of a variable planning horizon is proposed in order to construct an appropriate…

We propose an unconstrained optimization method based on the well-known primal-dual hybrid gradient (PDHG) algorithm. We first formulate the optimality condition of the unconstrained optimization problem as a saddle point problem. We then…

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…